You applied for your dream job and just found out you got it. Your contract states that you will be making $36,000 a year. To bu
dget your expenses, you figure out that your tax rate is 15%, your insurances will be $250 a month, and you want to put 4% away for your retirement. What is your monthly gross income per month, monthly taxes, monthly insurance, monthly retirement and net income (after deducting taxes, insurance and retirement) each month?
Doing some research, you decide you want to spend 25% of your monthly net income on an apartment. What is your monthly budget for housing?
You estimate that it will cost you $220 a month to eat and your car payment is $220 a month. What percentage of your net income are your eating expenses and car payment each?
After you worked for a year, you receive a 10% raise, but your health insurance increased to $300 a month and you want to now put 5% away for retirement. What is your new yearly gross income, your monthly gross income, monthly taxes, ,monthly insurance, monthly retirement and your new net income per month?
Continuing from number 4, you decided to support your favorite charity by donating $50 a month. What percentage of your new net income is this?
Continuing from number 4, you decide to take some dance lessons for fun, but want to
spend no more than 2% of your monthly budget (monthly net income) on the dance lessons. How much can you afford to spend?
How much money do you have left at the end of the month assuming your rent, car payment, food budgets, did not increase and you are giving to your charity and paying for dance lessons; how much to you have left for your personal use?
The company that you worked for is being forced to take 4% of your salary a month and put in a Retirement Savings Plan tax free (you will not pay taxes on this 4% - this amount will be taken off the top leaving a new amount as your monthly gross, etc). You still want to keep putting 5% away for retirement as you originally planned. What does your monthly budget look like now? The amount of housing allowance, food and car payment has not changed but the percentage has. Don't forget you are still paying for dance lessons.
Doing some research, you decide you want to spend 25% of your monthly net income on an apartment. What is your monthly budget for housing?
You estimate that it will cost you $220 a month to eat and your car payment is $220 a month. What percentage of your net income are your eating expenses and car payment each?
After you worked for a year, you receive a 10% raise, but your health insurance increased to $300 a month and you want to now put 5% away for retirement. What is your new yearly gross income, your monthly gross income, monthly taxes, ,monthly insurance, monthly retirement and your new net income per month?
Continuing from number 4, you decided to support your favorite charity by donating $50 a month. What percentage of your new net income is this?
Continuing from number 4, you decide to take some dance lessons for fun, but want to
spend no more than 2% of your monthly budget (monthly net income) on the dance lessons. How much can you afford to spend?
How much money do you have left at the end of the month assuming your rent, car payment, food budgets, did not increase and you are giving to your charity and paying for dance lessons; how much to you have left for your personal use?
The company that you worked for is being forced to take 4% of your salary a month and put in a Retirement Savings Plan tax free (you will not pay taxes on this 4% - this amount will be taken off the top leaving a new amount as your monthly gross, etc). You still want to keep putting 5% away for retirement as you originally planned. What does your monthly budget look like now? The amount of housing allowance, food and car payment has not changed but the percentage has. Don't forget you are still paying for dance lessons.
1 answer:
Answer:
see attached
Step-by-step explanation:
A spreadsheet is a useful tool for keeping track of the numbers. A picture of one is attached.
We have assumed that the dollar amount for housing computed in the first part remains the same (though the percentage changes). If that is not the case, you'll have to recompute.
Likewise, we assume that the "5%" retirement amount remains 5% of the nominal salary, rather than 5% of the salary after the mandatory retirement deduction. Similarly, we assume dance lessons remain at their original amount, and were not reduced when the company began taking mandatory retirement.
Feel free to build your own spreadsheet and recompute as needed for any assumptions I got wrong, or for any additional scenarios.
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Answer:
1. H0: P1 = P2
2. Ha: P1 ≠ P2
3. pooled proportion p = 0.542
4. P-value = 0.0171
5. The null hypothesis failed to be rejected.
At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .
6. The 99% confidence interval for the difference between proportions is (-0.012, 0.335).
Step-by-step explanation:
We should perform a hypothesis test on the difference of proportions.
As we want to test if there is significant difference, the hypothesis are:
Null hypothesis: there is no significant difference between the proportions (p1-p2 = 0).
Alternative hypothesis: there is significant difference between the proportions (p1-p2 ≠ 0).
The sample 1 (science), of size n1=135 has a proportion of p1=0.607.
The sample 2 (math), of size n2=92 has a proportion of p2=0.446.
The difference between proportions is (p1-p2)=0.162.
The pooled proportion, needed to calculate the standard error, is:
The estimated standard error of the difference between means is computed using the formula:
Then, we can calculate the z-statistic as:
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
As the P-value (0.0171) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .
We want to calculate the bounds of a 99% confidence interval of the difference between proportions.
For a 99% CI, the critical value for z is z=2.576.
The margin of error is:
Then, the lower and upper bounds of the confidence interval are:
The 99% confidence interval for the difference between proportions is (-0.012, 0.335).